Self-resonant modes in Josephson junctions with a phase discontinuity

We extend the theory of self-resonances in short Josephson junctions to the case of a piecewise constant critical current density and a κ discontinuity in the Josephson phase. We calculate the amplitude of the self-resonances as a function of applied magnetic field by using an extension of the approach introduced by Kulik for conventional Josephson junctions (I. O. Kulik, JETP Lett. 2, 84 (1965)). The theory given here agrees with existing experiments on superconducting–insulator–ferromagnet–superconductor 0–π Josephson junctions. The results are relevant to the characterization of all modern 0–π junctions as well as 0–κ junctions with artificially created phase discontinuities: high-temperature grain boundary junctions, junctions with a ferromagnetic barrier, and junctions with current injectors.

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